Video data have become the main data traffic on the Internet, and their traffic is increasing explosively every year, thus increasing the pressure of video transmission. Video coding technology has become the key to compressing original videos. As an indispensable technology, rate control plays an important role in stabilizing video stream transmission. Rate control (RC) is part of rate distortion optimization (RDO) whose job is to find the optimal solution based on balancing rate and distortion. It not only needs to consider the buffer and network status but also adjust the corresponding bit rate according to the video content. This paper reviews the related technologies of rate control under high efficiency video coding (HEVC) and versatile video coding (VVC) standards so that subsequent researchers can quickly understand the field and promote the development of rate control algorithms. Firstly, the paper summarizes the various aspects of RC, including basic principles, rate-distortion models, major processes, and performance criteria. Secondly, the paper surveys, in detail, the research progress in the field of rate control and analyzes several mainstream research directions. Thirdly, we carry out relevant experiments on the standard reference software and analyze and discuss the experimental results of the existing studies. Finally, we look ahead to the future trends of rate control and provide feasible improvement suggestions.